1. Field of the Invention
This invention relates to image processing apparatus, particularly of the type in which a digital representation of an image is filtered into a plurality of sub-bands in the two-dimensional spatial frequency domain.
2. Description of the Prior Art
It is known to use multi-tap digital finite impulse response (FIR) filters in the field of image processing. The filters operate on successive data elements representing respective digital samples of a scanned image. An element at the output of the filter represents a weighted sum of a predetermined number of equispaced elements or samples in the unfiltered data. The frequency response of the filter can be determined in advance by selecting a suitable number of elements to be included in the sum (that is, a suitable tap length) and by deriving appropriate weighting values or filter coefficients using known mathematical techniques.
A recently proposed use of these filtering techniques is to filter a digital representation of an image into a number of sub-bands in the two-dimensional spatial frequency domain. In this approach a spatial (two-dimensional) sub-band filtering arrangement divides an input video signal into a plurality of uncorrelated sub-bands each containing the spatial frequency content of the image in a respective one of a plurality of areas of a two dimensional frequency plane. The separate sub-bands may then be processed separately for the purposes of transmission or storage. At the reconstruction stage the sub-bands are interpolated and filtered before being added together to reproduce the original image, or at least an approximation of it. To achieve satisfactory results it is important that the filters used for interpolation are mathematically complementary to the decimation filters. The sub-band filtering approach has a number of useful features, particularly relating to the ease with which the resulting filtered data can be compressed for transmission or storage.
A data compression system incorporating sub-band filtering can make use of the fact that in the two-dimensional spatial frequency domain, low spatial frequency components of a picture are much more important to the perceived quality of a reconstructed picture than are components at high spatial frequency. To achieve data compression it has been proposed to encode the high spatial frequency sub-bands to a lower precision than those corresponding to low spatial frequency.